From Elasticity to Hypoplasticity: Dynamics of Granular Solids

"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well with models from soil mechanics

SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common nonsmooth functions arising in the applications such as the Euclidean norm, the maximum eigenvalue function and the least squares functions with $\ell_1$-regularization or elastic net regularization used in statistics and compressed sensing. We show that, under commonly used strict feasibility conditions, the optimal value and an optimal solution of SOS-convex semi-algebraic programs can be found by solving a single semi-definite programming problem (SDP). We achieve the results by using tools from semi-algebraic geometry, convex-concave minimax theorem and a recently established Jensen inequality type result for SOS-convex polynomials. As an application, we outline how the derived results can be applied to show that robust SOS-convex optimization problems under restricted spectrahedron data uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP relaxation result for restricted ellipsoidal data uncertainty and answers the open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a robust solution from the semi-definite programming relaxation in this broader setting

Dynamic Linkages in Credit Risk: Modeling the Time-Varying Correlation between the Money and Derivatives Markets over the Crisis Period

This paper examines the dynamic linkages in credit risk between the money market and the derivatives market during 2004–9. We use the T-bill–Eurodollar (TED) spread to measure credit risk in the money market and the credit default swap (CDS) index spread for the derivatives market. The linkages are measured by a dynamic conditional correlation–Glosten–Jagannathan–Runkle–generalized auto regressive conditional heteroscedasticity model. The results show that the correlation between the TED spread and the CDS index spread fluctuated around zero prior to the crisis. While the correlation increased before the crisis, it moved notably higher during the crisis. Finally, the correlation fell in early 2009 but persisted at a level between 0.05 and 0.1, higher than the precrisis period

Monte-Carlo approach to calculate the proton stopping in warm dense matter within particle-in-cell simulations

A Monte-Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. The model is based on multiple binary-collisions among electron-electron, electron-ion and ion-ion, taking into account contributions from both free and bound electrons, and allows to calculate particle stopping in much more natural manner. At low temperature limit, when ``all'' electron are bounded at the nucleus, the stopping power converges to the predictions of Bethe-Bloch theory, which shows good consistency with data provided by the NIST. With the rising of temperatures, more and more bound electron are ionized, thus giving rise to an increased stopping power to cold matter, which is consistent with the report of a recently experimental measurement [Phys. Rev. Lett. 114, 215002 (2015)]. When temperature is further increased, with ionizations reaching the maximum, lowered stopping power is observed, which is due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.Comment: 6 pages, 4 figure

The Dependence Structure in Credit Risk between Money and Derivatives Markets: A Time-Varying Conditional Copula Approach

Purpose The purpose of this paper is to examine the dynamic dependence structure in credit risk between the money market and the derivatives market during 2004-2009. The authors use the TED spread to measure credit risk in the money market and CDS index spread for the derivatives market. Design/methodology/approach The dependence structure is measured by a time-varying Gaussian copula. A copula is a function that joins one-dimensional distribution functions together to form multivariate distribution functions. The copula contains all the information on the dependence structure of the random variables while also removing the linear correlation restriction. Therefore, provides a straightforward way of modelling non-linear and non-normal joint distributions. Findings The results show that the correlation between these two markets while fluctuating with a general upward trend prior to 2007 exhibited a noticeably higher correlation after 2007. This points to the evidence of credit contagion during the crisis. Three different phases are identified for the crisis period which sheds light on the nature of contagion mechanisms in financial markets. The correlation of the two spreads fell in early 2009, although remained higher than the pre-crisis level. This is partly due to policy intervention that lowered the TED spread while the CDS spread remained higher due to the Eurozone sovereign debt crisis. Originality/value The paper examines the relationship between the TED and CDS spreads which measure credit risk in an economy. This paper contributes to the literature on dynamic co-movement, contagion effects and risk linkages

Monte-Carlo approach to calculate the ionization of warm dense matter within particle-in-cell simulations

A physical model based on a Monte-Carlo approach is proposed to calculate the ionization dynam- ics of warm dense matters (WDM) within particle-in-cell simulations, and where the impact (col- lision) ionization (CI), electron-ion recombination (RE) and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal re- laxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different composi- tions. The proposed model is implemented into a particle-in-cell (PIC) code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium in the WDM regime, i) the averaged ionization degree increases by including IPD; while ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures, and shows good agreements with that generated from Saha-Boltzmann model or/and FLYCHK code.Comment: 7 pages, 4 figure